Oh, bless her heart. I have to say I don't have a 9 year old girl, I have a 9 year old boy, but I would put his drama and emotions up against any girl's lol. I love that about him but it does cause him some heartache occasionally.
His "huge fights" (and remember that term is relative) are usually along the lines of "I was jumping on the trampoline and Mason said I kicked him and I said no I didn't and he said he was going to tell his mom and that would be a LIE because I didn't do anything and he's a big JERK FACE!!!!!" (with full tears and red face lol)
99% of the time (while I love that he shares with me so freely) it is nothing that an adult needs to get involved in. I strongly feel he should deal with these things himself and I don't get involved unless it is a safety issue. Or if I know that other adults have been drug into it already and he needs my backup. I just coach him on how to handle it (including an apology for losing his temper if needed) and send him on his way, after letting him cool off for a few minutes. At this age it's all about teaching them how to deal with these things themselves. Friendships, all the emotions they're feeling, they need to be shown how to handle it all. They don't need it handled for them.
ETA: I guess your SWH was probably directed at me too. I sense a lot of disapproval in your post, from your daughter keeping things private, to how you feel the school is doing their job. And now you're disapproving of us telling you what we would do. You say you "intend" to stay out of your granddaughter's issues, but your tone and comments suggest you don't really believe that you should have to. Which is what we all picked up on, and is why many of us stated it's best to stay out of it. You don't really seem willing to do that, despite what you say.